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Capacitive displacement-sensing gauges are known in the art. These gauges use the change in capacitance between a capacitive displacement probe (probe) and the structure over which it is positioned (target) to measure the change in distance between the probe and the target.
These gauges are characterized by the equation that describes the capacitance of a parallel-plate capacitor.                     C        =                              k            ⁢                          xe2x80x83                        ⁢                          ϵ              0                        ⁢            A                    d                                    (        1        )            
where
C=capacitance
∈hd 0=permittivity of free space
k=dielectric constant
A=plate area
d=distance between plates
When using a capacitive-displacement probe, the plate area, which is the area of the probe""s sensing element, is held constant, and the dielectric constant, typically air, is also constant. With this configuration, distance (d) is inversely proportional to the capacitance (C).
The voltage (v) and current (i) in a capacitor are related by equation 2.                     v        =                  i                      s            ⁢                          xe2x80x83                        ⁢            C                                              (        2        )            
where s is the complex frequency variable
When Equation 1 is substituted into Equation 2, v is expressed by equation 3.                     v        =                              i            ⁢                          xe2x80x83                        ⁢            d                                s            ⁢                          xe2x80x83                        ⁢            k            ⁢                          xe2x80x83                        ⁢                          ϵ              0                        ⁢            A                                              (        3        )            
Equation 3 implies that if frequency (s) and current (i) are held constant, voltage v is proportional to the distance d between the probe and target. This relationship leads to an operational mode where capacitive displacement probes are commonly driven with a constant current, and the voltage across the probe provides an output that varies linearly as the distance varies. Because the voltage is most likely not directly usable, it is usually processed, for instance, by a unity-gain buffer before being used.
To ensure that a linear relationship between the circuit""s transfer function and distance holds in practice, the probe must be guarded to prevent parasitic capacitances from appearing in parallel with the probe capacitance. Total probe capacitances are often tenths or even hundredths of a picofarad. The linear relationship between the circuit""s transfer function and distance is further ensured by utilizing a high impedance input stage in the circuit receiving the input. When a unity-gain buffer is connected to the probe, the buffer amplifier""s power-supply connections must be bootstrapped to ensure that the input impedance is high enough to maintain the transfer function of the gauge.
The frequency response of the unity-gain buffer should be flat and wideband to track the capacitance. Since the power-supply characteristics affect the buffer""s frequency response, it is necessary to utilize a more costly and complex power-supply in this configuration.
Another way to connect to the probe and maintain the desired transfer function is to use a differential amplifier, such as an operational amplifier, with a grounded output in place of the unity-gain buffer. In prior art, in order to be able to ground the output, the amplifier is powered by a floating power supply. The floating power supply is an additional component that increases the size and complexity of the gauge system. The required transformer may need to be large, expensive and may be susceptible to stray electric and magnetic fields. To achieve the desired function, it may need to be custom made.
A capacitive displacement-sensing gauge in which the transducer interface stage generates its own bootstrapping voltages provides a smaller more cost-effective gauge. A differential amplifier with a grounded output is used as a transducer interface stage and power and common connections to the stage are made via a 3-winding transformer in which the three windings are equal in turns and are closely coupled. The current that flows to ground through the grounded output of this stage by necessity flows through a winding of the transformer, causing the common voltage and both supply voltages to be perfectly bootstrapped.
No active circuitry, with its concomitant limitations in phase and frequency response, is required. Cost and size are reduced by elimination of active circuitry and/or the means necessary to create a floating supply. Reliability is improved by reducing the number of circuit elements that are required. Other aspects, features, and advantages of the present invention are disclosed in the detailed description that follows.